Generic Downwards Accumulations (2000)
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| Venue: | Science of Computer Programming |
| Citations: | 17 - 2 self |
BibTeX
@INPROCEEDINGS{Gibbons00genericdownwards,
author = {Jeremy Gibbons},
title = {Generic Downwards Accumulations},
booktitle = {Science of Computer Programming},
year = {2000},
pages = {200--0},
publisher = {Springer-Verlag}
}
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Abstract
. A downwards accumulation is a higher-order operation that distributes information downwards through a data structure, from the root towards the leaves. The concept was originally introduced in an ad hoc way for just a couple of kinds of tree. We generalize the concept to an arbitrary regular datatype; the resulting denition is co-inductive. 1 Introduction The notion of scans or accumulations on lists is well known, and has proved very fruitful for expressing and calculating with programs involving lists [4]. Gibbons [7, 8] generalizes the notion of accumulation to various kinds of tree; that generalization too has proved fruitful, underlying the derivations of a number of tree algorithms, such as the parallel prex algorithm for prex sums [15, 8], Reingold and Tilford's algorithm for drawing trees tidily [21, 9], and algorithms for query evaluation in structured text [16, 23]. There are two varieties of accumulation on lists: leftwards and rightwards. Leftwards accumulation ...
